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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8.3, Problem 78E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Health After a person exercises for a few minutes, the velocity v (in liters per second) of airflow into and out of the lungs during a respiratory cycle is given by

v = 1.75 sin π t 2 where t is the time (in seconds). Inhalation occurs when v > 0, and exhalation occurs when v < 0.

(a) Find the time for one full respiratory cycle.

(b) Find the number of cycles per minute.

(c) Find the velocities of airflow when t = 2 and t = 3 without using a calculator.

(d) Use a graphing utility to find the velocity of airflow when t = 1.5.

(e) Use a graphing utility to graph the velocity function.

(a)

To determine

To calculate: The time for one full respiratory cycle if the velocity of airflow is v=1.75sinπt2.

Explanation

Given Information:

The velocity of airflow into and out from the lungs is v=1.75sinπt2.

Formula used:

The period of sine function is defined as,

Period=2πb

Calculation:

Consider the function,

v=1.75sinπt2.

Compare the provided function with the standard function, v=asinbt. Here, a=1

(b)

To determine

To calculate: The number of cycles per minute if the velocity of airflow into and out from the lungs is v=1.75sinπt2.

(c)

To determine

To calculate: The velocities of airflow when t=2 and t=3 if the velocity of airflow into and out from the lungs is v=1.75sinπt2.

(d)

To determine

To calculate: The velocity of airflow when t=1.5 if the velocity of airflow into and out from the lungs is v=1.75sinπt2.

(e)

To determine

To graph: The graph of the function if the velocity of airflow into and out from the lungs is v=1.75sinπt2.

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 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Fill in each blank, rounding each result of three significant digits when necessary: 1.8ft3=in3

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Find the exact areas of the shaded regions in Exercises 27 to 31.

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Problems 1 through 10 refer to triangle ABC, which is not necessarily a right triangle. Find all the missing pa...

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Using Exhibit 20-6, Mutual Fund Quotation Table, on page 693, explain the information listed for the John Hanco...

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In Exercise 21-24, find the expected payoff E of each game whose payoff matrix and strategies P and Q for the ...

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For Review Exercises 7 to 11, use the given information to name the segments that must be parallel. If there ar...

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